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In [[algebraic geometry]], the  '''Barth–Nieto quintic''' is a [[quintic]] [[3-fold]] in 4 (or sometimes 5) dimensional [[projective space]] studied by {{harvtxt|Barth|Nieto|1994}} that is the [[Hessian]] of the [[Segre cubic]]. The Barth–Nieto quintic is the closure of the set of points (''x''<sub>0</sub>:''x''<sub>1</sub>:''x''<sub>2</sub>:''x''<sub>3</sub>:''x''<sub>4</sub>:''x''<sub>5</sub>) of '''P'''<sup>5</sub> satisfying the equations
:<math>\displaystyle x_0+x_1+x_2+x_3+x_4+x_5= 0</math>
:<math>\displaystyle x_0^{-1}+x_1^{-1}+x_2^{-1}+x_3^{-1}+x_4^{-1}+x_5^{-1} = 0.</math>
 
The Barth–Nieto quintic is not rational, but has a smooth model that is a [[Calabi-Yau manifold]].
 
==References==
*{{Citation | last1=Barth | first1=W. | last2=Nieto | first2=I. | title=Abelian surfaces of type (1,3) and quartic surfaces with 16 skew lines | mr=1257320 | year=1994 | journal=Journal of Algebraic Geometry | issn=1056-3911 | volume=3 | issue=2 | pages=173–222}}
 
{{DEFAULTSORT:Barth-Nieto quintic}}
[[Category:Threefolds]]
 
 
{{Mathematics-stub}}

Latest revision as of 19:19, 11 March 2013

In algebraic geometry, the Barth–Nieto quintic is a quintic 3-fold in 4 (or sometimes 5) dimensional projective space studied by Template:Harvtxt that is the Hessian of the Segre cubic. The Barth–Nieto quintic is the closure of the set of points (x0:x1:x2:x3:x4:x5) of P5 satisfying the equations

The Barth–Nieto quintic is not rational, but has a smooth model that is a Calabi-Yau manifold.

References

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